The apparent resistivity tensor

Various attempts have been made to combine the results of resistivity measurements from two similarly located current sources of different orientation. The essential point that needs to be recognized is that there are two parameters determined from each current source - a total of four parameters in all. Although it may be diagnostically convenient to combine these in some manner to derive a single parameter, this process essentially discards valuable information. In this note we show that these four parameters together define a tensor apparent resistivity at each field point. This tensor contains all the information from both current sources. Other definitions of apparent resistivity may be extracted as special properties of the apparent resistivity tensor.